On 11/17/2003 04:13 PM, Ludwik Kowalski wrote:
>
> Will it continue move in the same way
> in which it was when the bob was attached or not?
> Keep in mind that zero mass particles have no
> weight and their behavior is not subjected to
> Newton's first law.
Here's how I look at it: Strings are never massless.
When we mention a "massless" string, it's a slightly
sloppy shorthand for "string with mass negligible in
comparison to the bob and other things of interest".
Now, when you suddently detach the bob, the formerly
negligible mass is now not negligible at all. The
mass of the string is the only interesting mass in
the problem.
So you don't need to worry about the pathological
behavior of a massless string. Assume it has a
constant mass-per-unit-length rho and do the
physics. It's an interesting problem. In the
absence of gravity it's trivial. In the presence
of gravity it's highly nontrivial: the string
takes on a complex shape due to the interplay
between gravity and the non-uniform tension.
The shape is, unsurprisingly, independent of rho,
so at the end of the calculation you can take the
limit as rho -> zero if you like. Or not, since
it doesn't matter.
> I know that this situation is purely hypothetical.
I wouldn't call it hypothetical at all. There are
lots of engineering problems with similar structure.
Think for instance about the huge and highly nonuniform
tension (not to mention other forces) in a rapidly
spinning propeller.